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2 Public Key CryptographyTwo keysPrivate key known only to individualPublic key available to anyoneIdeaConfidentiality:encipher using public key,decipher using private keyIntegrity/authentication:encipher using private key,decipher using public oneRAITM. Chatterjee

3 RequirementsGiven the appropriate key, it must be computationally easy to encipher or decipher a messageIt must be computationally infeasible to derive the private key from the public keyIt must be computationally infeasible to determine the private key from a chosen plaintext attackRAITM. Chatterjee

4 Public-Key Cryptographypublic-key/two-key/asymmetric cryptography involves the use of two keys:a public-key, which may be known by anybody, and can be used to encrypt messages, and verify signaturesa private-key, known only to the recipient, used to decrypt messages, and sign (create) signaturesRAITM. Chatterjee

7 Why Public-Key Cryptography?developed to address two key issues:key distribution – how to have secure communications in general without having to trust a KDC with your keydigital signatures – how to verify a message comes intact from the claimed senderpublic invention due to Whitfield Diffie & Martin Hellman at Stanford in 1976known earlier in classified communityRAITM. Chatterjee

9 Security of Public Key Schemeslike private key schemes brute force exhaustive search attack is always theoretically possiblebut keys used are too large (>512 bits)not comparable to symmetric key sizessecurity relies on a large enough difference in difficulty between easy (en/decrypt) and hard (to cryptanalyze) problemsrequires the use of very large numbershence is slow compared to secret key schemesRAITM. Chatterjee

11 Diffie-Hellman Key Exchangea public-key distribution schemecannot be used to exchange arbitrary messagesrather it can establish a common keyknown only to the two participantsvalue of key depends on the participants (and their private and public key information)based on exponentiation in a finite (Galois) field (modulo a prime or a polynomial) - easysecurity relies on the difficulty of computing discrete logarithms (similar to factoring) – hardRAITM. Chatterjee

12 Generating the Diffie-Hellman public keyDiffie-Hellman SetupGenerating the Diffie-Hellman public keyThe Diffie-Hellman system allows Alice and Bob to agree on a key even when Eve is listening to everything they say to each other.Alice and Bob need to agree on a prime number p, which they can do by simply sending it to each other.Eve is allowed to learn this number p. In practice the number p is often simply advertised somewhere public.RAITM. Chatterjee

13 Generators & Public KeyGiven a prime number p, it is possible to come up with a number g (the so-called generator) with a very interesting property. Every number between 1 and p-1 can be written as a power of g when calculating modulo p. For example, using p = 5 the generator is 2, because20 = 121 = 222 = 423 = 3 (because 8 = 3 mod 5)Alice and Bob agree in the same way on a generator g for the numbers between 1 and p-1.The numbers p and g serve as the public key.RAITM. Chatterjee

19 Disadvantages: Expensive exponential operationDoS possible.The scheme itself cannot be used to encrypt anything – it is for secret key establishment.No authentication, so you can not sign anything …RAITM. Chatterjee